Section 3.4 ~ A Few Cautions About Graphics Introduction to Probability and Statistics Ms. Young ~ room 113

Objective Sec. 3.4 In this section you will learn how to evaluate graphics and identify common ways in which graphics can be misleading

Perceptual Distortions Sometimes graphics are used to represent an increase or a decrease over time The way that they are drawn can distort the perception of the actual increase or decrease  Example ~ The following graphics are used to represent the decrease in the value of a dollar in comparison to the year 1980 The intention was that the length’s of the dollar bill would represent the ratio, but our eyes are drawn to the area of the dollar bill which is very deceiving because it appears as though it decreased much more than it did Sec. 3.4

Perceptual Distortions Cont’d…  Example ~ The following graphics are used to represent the increase in the number of homes with cable television from 1980 to 2005 The intention was that the length’s of the TV’s would represent the comparison, but our eyes are drawn to the volume of the TV’s which are very deceiving because it appears as though there was a much larger increase than there really was Sec. 3.4 Homes with Cable TV 18 million homes73 million homes

Watch the Scales Be cautious that the scales on the horizontal and/or vertical axes are uniform  If they are not, the graph may be misleading on the first impression  Example ~ The following graph represents the percentage of people owning their homes from It appears at first that the years spanning from 1960 to 2000 had a greater increase in home ownership than the more recent years, but if you look closer, the horizontal scale is not uniform  The first five categories are a decade apart, but the last two categories are only a couple years apart Sec. 3.4

Watch the Scales Cont’d… Example ~ the following graph represents the percentage of college students between 1910 and 2005 who were women  It appears as though there was a huge increase of women attending college after 1950, but if you look at the vertical scale, you should realize that it does not begin at zero and does not end at 100% If you redraw the graph with the vertical axis covering the full range from 0% to 100%, you can see that the increase is not as substantial as it originally seemed to be. Sec. 3.4

Exponential Scales Be cautious about whether the scale is exponential or not  Example ~ the following graph represents the speed of a computer (calculations per second) from 1950 to 2000 The first graph appears to be increasing linearly, but if you look closer at the scale, you realize that each tick mark represents a tenfold increase (grows by a power of 10)  These exponential scales are useful in displaying data that vary over a huge range of values  If you just used an ordinary graph, it makes it very hard to see any detail in the early years Sec. 3.4 Exponential graph Ordinary graph

Percentage Change Graphs If the scale represents percent change (percent increase or percent decrease), a spike or a drop in the chart doesn’t represent the value increasing or decreasing, but rather the rate at which it changed  Example ~ the following graph represents the percent change from the previous year in college costs between private and public colleges It appears as though the “price” dropped drastically for public colleges after 2004, but really it just means that the percent increase wasn’t as high as it was in previous years If you redraw this graph with the actual cost as the scale, you can see that the cost steadily rises and doesn’t decrease at all Sec. 3.4

Pictographs Pictographs are graphs that are enhanced with additional artwork  Although it may make the graph more appealing, it can also distract or mislead  Example ~ the following diagram represents the world population from 1804 to 2054 The bars represent the population fairly, but the pictures of people lining the globe give the impression that the population increases and then falls In addition to the pictures being misleading, this graph does not use a uniform horizontal scale, which gives the impression that population has been rising (and will continue to rise) linearly Sec. 3.4